Table of contents

Chapter I considers cyclotron oscillations of an equilibrium plasma (the cyclotron heating problem). It is devoted mainly to the analysis of processes that lead to energy exchange between oscillations and a plasma in cyclotron resonance in an inhomogeneous magnetic field. According to present-day concepts, such an exchange is effected by excitation of modulated beams. The oscillations due to individual beams are analogous to the known Van Kampen waves. In the presence of a thermal spread of the plasma-particle velocity, the interference quenches these oscillations. As a result, the energy drawn by the plasma from the cyclotron wave takes on a thermal (random) form. An appendix (at the end of the article) traces the analogy with Cerenkov resonance in an inhomogeneous plasma and with surface absorption of the oscillations incident on an abrupt plasma boundary (anomalous skin effect). Chapter II summarizes earlier results on the analysis of the stability of a plasma not in thermal equilibrium situated in the inhomogeneous field of a magnetic trap. It was shown in the earlier papers that, depending on the conditions on the plasma boundaries, an increase in the inhomogeneity of the magnetic field can lead to either a lowering of the increment of the unstable natural oscillations (oscillation-reflecting boundaries), or to their total stabilization (absorbing boundaries). Two approaches to the investigation of stability are compared in the review, viz., analysis of the natural oscillations and an investigation of the evolution of the initial perturbations with time.

The article reviews the present status of the theory of weak interactions of elementary particles at high energies and large momentum transfers; in the spatial picture this corresponds to short distances. The usual four-fermion V-A theory of weak interactions and the theory with intermediate W boson are considered. Special attention is paid to virtual processes, particularly hadron-lepton and nonlepton weak interactions (weak neutral currents, K_L° and K_S° meson mass difference, hadronic processes with strangeness and parity change). It is shown that a theoretical investigation of these processes in the comparison of its results with experiment leads to serious contradictions in the theory. Different ways out of the difficulties existing in the theory are discussed.

In this article a critical analysis is given of basic geometric concepts as applied to the physics of the microcosmos. The article begins with an outline of geometry in macroscopic physics. This part is based on the classical papers of H. Poincare, A. Einstein, and A. A. Fridman. An indication of possible limitations on the concept of a point event associated with limiting densities of matter represents new material. Subsequently localization of elementary particles is discussed and limits of possible accuracy are indicated. In the article it is emphasized that the logical structure of local quantum field theory presupposes the existence of particles of arbitrarily large mass. The existence of "maximons"–particles of a limiting, but finite mass–strong gravitation (collapse of particles), instability of particles with respect to decay due to the weak interaction (this interaction can become strong for very heavy particles and can lead to lead to total instability of such a particle). In the conclusion of the article two features of a nonlocal field theory are considered. In this theory the coordinates of a point event are operators, while momentum space remains a numerical space (either curved or flat). The first variant presupposes commutation conditions for the coordinates of a point (the Snyder-Kadyshevskii theory), while the second variant presupposes anticommutation conditions (the author's theory).

The review considers, on the basis of a unified approach, the problem of Brownian motion in nonlinear dynamic systems, including a linear oscillator acted upon by random forces, parametric resonance in an oscillating system with random parameters, turbulent diffusion of particles in a random-velocity field, and diffusion of rays in a medium with random inhomogeneities of the refractive index. The same method is used to consider also more complicated problems such as equilibrium hydrodynamic fluctuations in an ideal gas, description of hydrodynamic turbulence by the method of random forces, and propagation of light in a medium with random inhomogeneities. The method used to treat these problems consists of constructing equations for the probability density of the system or for its statistical moments, using as the small parameter the ratio of the characteristic time of the random actions to the time constant of the system (in many problems, the role of the time is played by one of the spatial coordinates). The first-order approximation of the method is equivalent to replacement of the real correlation function of the action by a δ function; this yields equations for the characteristics in closed form. The method makes it possible to determine also higher approximations in terms of the aforementioned first-order small parameter.

Recent experimental studies of kinetic processes in dense gases and in plasma have stimulated the development of the theory of nonideal gases or plasmas. By now, a kinetic theory has been developed for nonideal monatomic gases of medium density, as well as a kinetic theory of weakly nonideal fully ionized plasma. The present review is devoted to a systematic exposition of these questions. The kinetic theory of nonideal gases of low density is constructed on the basis of a generalized Boltzmann kinetic equation (in the pair-collision approximation) and the Cho-Uhlenbeck kinetic equation (in the triple-collision approximation). The kinetic equations for denser gases have an essentially different structure than the ordinary kinetic equations. This is caused by the impossibility of using the ordinary scheme, owing to the divergences of the collision integrals in the higher approximations in the density. The article presents a kinetic theory of a weakly nonideal plasma. Particular attention is paid to the possibility of constructing classical and quantum kinetic equations without assuming the particle interaction to be small at short distances, since the particle interaction at short distances plays an essential role in a nonideal plasma. A. prominent place is occupied in the review by an exposition of the kinetic theory of fluctuations in nonideal gases and plasma. Certain problems in the kinetic theory of nonideal systems are considered.

The present review is devoted to discussion of the principal stages of development of mirror electron microscopy. In the mirror electron microscope (MEM) the electron beam is reflected in a retarding electric field near the sample surface, and as a result the object being studied is not subjected to bombardment by the probe particles. This permits information to be obtained on the geometrical relief of the surface and the microfields in it. The review discussses the problems of MEM design, the different modes of operation, and questions of the limiting resolution. The theory of contrast formation for the geometrical relief and also for electric and magnetic microfields is discussed in detail. Experimental data are presented on investigation of a broad class of objects—semiconductors, dielectrics, and magnetic structures—in MEM. Various techniques for quantitative measurement of static and dynamic microfields on the surface of solid samples are described.